I want to simply drag keyframes from one part of my timeline to another. I shrink the timeline down so I can see more of it, though that does not make it much easier because I need it to be even smaller. Is there another way of doing this?

In 2015 just put your mouse over the time ruler and roll the mouse wheel to zoom in and out of the timeline. If you have an enhanced wheel you can use the left and right movement of the wheel or drag your finger over a trackpad go scroll through time. You can zoom clear to the frame level if you want, then you can click and drag around keyframes.

If this still doesn't give you enough room you can use the icons at the very bottom left of the timeline to expand or contract the columns that are visible on the left. You can also use the ~ key to make the timeline full screen. It's all part of getting around in the UI, which should be part of your basic AE training.